Simplified form of Voltage Formula

AI Thread Summary
The discussion centers on the voltage formula related to electric fields, specifically the equation Vb-Va = -∫_a^b E dl. A user questions the simplification for a positively charged conducting sphere, suggesting an alternative expression. They initially express confusion about the integral limits and the resulting formula. Ultimately, the user resolves their misunderstanding and acknowledges their error. The conversation highlights the importance of correctly applying integral limits in voltage calculations.
Typhon4ever
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In my book it gives the relationship between voltage and electric field as Vb-Va= -\int _a^{b} E dl which for a positively charged conducting sphere Q simplifies to \frac{Q}{4\pi\epsilon_0} (\frac{1}{b}-\frac{1}{a}) my questions is that shouldn't it be \frac{Q}{4\pi\epsilon_0} (\frac{1}{a}-\frac{1}{b})? The integral turns into \int _b^{a} what am I missing here?
 
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Nvmind I got it I feel stupid lol
 
It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.
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